100 citations · 495 across the 18 of their papers we have counts for
18 papers
Computation of the Time-Dependent Dirac Equation with Physics-Informed Neural Networks
Emmanuel Lorin, Xu Yang
We propose to compute the time-dependent Dirac equation using physics-informed neural networks (PINNs), a new powerful tool in scientific machine learning avoiding the use of appro…
Schwarz Waveform Relaxation Physics-Informed Neural Networks for Solving Advection-Diffusion-Reaction Equations
Emmanuel Lorin, Xu Yang
This paper develops a physics-informed neural network (PINN) based on the Schwarz waveform relaxation (SWR) method for solving local and nonlocal advection-diffusion-reaction equat…
Numerical quasi-conformal transformations for electron dynamics on strained graphene surfaces
F. Fillion-Gourdeau, E. Lorin, S. MacLean
The dynamics of low energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a…
Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces
Xavier Antoine, François Fillion-Gourdeau, Emmanuel Lorin +1
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along wit…
Nonlinear Nonperturbative Optics Model Enriched by Evolution Equation for Polarization
M. Lytova, E. Lorin, A. Bandrauk
In this work, we extend and analyze the nonperturbative Maxwell-Schrödinger-Plasma (MASP) model. This model was proposed to describe the high order optical nonlinearities, and the…
Domain Decomposition Method for the -body Time-Independent and Time-Dependent Schrödinger Equation
E. Lorin
This paper is devoted to the derivation of a pleasingly parallel Galerkin method for the time-independent -body Schrödinger equation, and its time-dependent version modeling mol…